Salt influences protein stability through electrostatic mechanisms as well as through nonpolar Hofmeister effects. In the present work, a continuum solvation based model is developed to explore the impact of salt on protein stability. This model relies on a traditional Poisson-Boltzmann (PB) term to describe the polar or electrostatic effects of salt, and a surface area dependent term containing a salt concentration dependent microscopic surface tension function to capture the non-polar Hofmeister effects. The model is first validated against a series of cold-shock protein variants whose salt-dependent protein fold stability profiles have been previously determined experimentally. The approach is then applied to HIV-1 protease in order to explain an experimentally observed enhancement in stability and activity at high (1M) NaCl concentration. The inclusion of the salt-dependent non-polar term brings the model into quantitative agreement with experiment, and provides the basis for further studies into the impact of ionic strength on protein structure, function, and evolution.